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Applying SEIR model without vaccination for COVID-19 in case of the United States, Russia, the United Kingdom, Brazil, France, and India 美国、俄罗斯、英国、巴西、法国和印度在不接种COVID-19疫苗的情况下应用SEIR模型
Q3 Mathematics Pub Date : 2021-02-01 DOI: 10.1515/em-2020-0036
Marwan Al-Raeei, M. S. El-daher, Oliya Solieva
Abstract Objectives: Compartmental models are helpful tools to simulate and predict the spread of infectious diseases. In this work we use the SEIR model to discuss the spreading of COVID-19 pandemic for countries with the most confirmed cases up to the end of 2020, i.e. the United States, Russia, the United Kingdom, France, Brazil, and India. The simulation considers the susceptible, exposed, infective, and the recovered cases of the disease. Method: We employ the order Runge–Kutta method to solve the SIER model equations-for modelling and forecasting the spread of the new coronavirus disease. The parameters used in this work are based on the confirmed cases from the real data available for the countries reporting most cases up to December 29, 2020. Results: We extracted the coefficients of the exposed, infected, recovered and mortality rate of the SEIR model by fitting the collected real data of the new coronavirus disease up to December 29, 2020 in the countries with the most cases. We predict the dates of the peak of the infection and the basic reproduction number for the countries studied here. We foresee COVID-19 peaks in January-February 2021 in Brazil and the United Kingdom, and in February-March 2021 in France, Russia, and India, and in March-April 2021 in the United States. Also, we find that the average value of the SARS-CoV-2 basic reproduction number is 2.1460. Conclusion: We find that the predicted peak infection of COVID-19 will happen in the first half of 2021 in the six considered countries. The basic SARS-CoV-19 reproduction number values range within 1.0158–3.6642 without vaccination.
目的:区室模型是模拟和预测传染病传播的有效工具。在这项工作中,我们使用SEIR模型讨论了截至2020年底确诊病例最多的国家(即美国、俄罗斯、英国、法国、巴西和印度)COVID-19大流行的传播情况。该模拟考虑了该疾病的易感、暴露、感染和恢复病例。方法:采用阶龙格-库塔法求解SIER模型方程,对新型冠状病毒的传播进行建模和预测。本工作中使用的参数基于截至2020年12月29日报告病例最多的国家可获得的真实数据中的确诊病例。结果:通过拟合收集到的截至2020年12月29日病例最多的国家的新型冠状病毒病真实数据,提取了SEIR模型的暴露率、感染率、康复率和死亡率系数。我们预测了感染高峰的日期和这里研究的国家的基本繁殖数。我们预计2021年1月至2月巴西和英国、2021年2月至3月法国、俄罗斯和印度以及2021年3月至4月美国将出现COVID-19高峰。SARS-CoV-2基本复制数的平均值为2.1460。结论:我们发现,预测的COVID-19感染高峰将出现在2021年上半年。在不接种疫苗的情况下,SARS-CoV-19的基本繁殖数值在1.0158-3.6642之间。
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引用次数: 8
Zealous clout of COVID-19: analytical research at sixes and sevens COVID-19的狂热影响:六和七的分析研究
Q3 Mathematics Pub Date : 2021-02-01 DOI: 10.1515/em-2020-0015
Madhu Raina
Abstract This New Year’s wake-up call warned us of Democles’ sword in the form of COVID-19, an epidemic turned pandemic. Seeming to reach a novel and awful landmark every day, governments across globe are fighting on toes to contain its spread. The pandemic is accelerating and information is being updated and changing by the hour. Till date shattering causalities across globe have been reported to World Health Organization. Nevertheless, the world is responding to this novel enemy with urgency and purpose. The challenge is great, but the response has been massive. Record characterisation and multiple sequences of this novel pathogen are being shared on global platform leading to a lot of diagnostics to get developed. Currently no treatment is effective against COVID-19 and there is a desperate need for international solidarity for valuable therapeutics. Present article briefs some milestones achieved by the killer virus thereby posing a challenge to medical science.
这个新年的警钟提醒我们,COVID-19是德谟克利斯之剑,一种流行病变成了大流行。似乎每天都在达到一个新的可怕的里程碑,全球各国政府都在努力控制其传播。疫情正在加速蔓延,信息每小时都在更新和变化。迄今为止,已向世界卫生组织报告了全球范围内令人震惊的伤亡人数。尽管如此,世界正在紧迫而坚定地应对这一新的敌人。挑战是巨大的,但反应是巨大的。这种新型病原体的记录特征和多个序列正在全球平台上共享,从而开发出许多诊断方法。目前没有针对COVID-19的有效治疗方法,迫切需要国际社会团结一致,寻找有价值的治疗方法。本文简要介绍了致命病毒取得的一些里程碑,从而对医学科学提出了挑战。
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引用次数: 0
The risk factors of COVID-19 in 50–74 years old people: a longitudinal population-based study 50-74岁人群感染COVID-19的危险因素:一项基于人群的纵向研究
Q3 Mathematics Pub Date : 2021-02-01 DOI: 10.1515/em-2021-0024
Hozhabr Jamali Atergeleh, M. Emamian, Shahrbanoo Goli, M. Rohani-Rasaf, H. Hashemi, A. Fotouhi
Abstract Objectives To investigate the risk factors of COVID-19 infection in a longitudinal study of a population aged 50–74 years. Methods Data were collected from Shahroud Eye Cohort study and the COVID-19 electronic registry in Shahroud, northeast Iran. Participants were followed for about 13 months and predisposing factors for COVID-19 infection were investigated using log binominal model and calculating relative risks. Results From the beginning of the COVID-19 outbreak in Shahroud (February 20, 2020) to March 26, 2021, out of 4,394 participants in the Eye Cohort study, 271 (6.1%) were diagnosed with COVID-19 with a positive reverse transcription polymerase chain reaction test on two nasopharyngeal and oropharyngeal swabs. Risk factors for COVID-19 infection included male gender (relative risk (RR) = 1.51; 95% confidence intervals (CI), 1.15–1.99), body mass index (BMI) over 25 (RR = 1.03; 95% CI, 1.01–1.05), and diabetes (RR = 1.31; 95% CI, 1.02–1.67). Also, smoking (RR = 0.51; 95% CI, 0.28–0.93) and education (RR = 0.95; 95% CI, 0.92–0.98) showed inverse associations. Conclusions Men, diabetics, and those with BMI over 25 should be more cognizant and adhere to health protocols related to COVID-19 prevention and should be given priority for vaccination.
目的通过对50 ~ 74岁人群的纵向研究,探讨COVID-19感染的危险因素。方法收集伊朗东北部shahoud地区shahoud眼队列研究和COVID-19电子登记处的数据。参与者随访约13个月,使用对数二项模型调查COVID-19感染的易感因素并计算相对风险。结果从2019冠状病毒病在沙赫鲁德暴发开始(2020年2月20日)到2021年3月26日,在眼睛队列研究的4394名参与者中,271人(6.1%)被诊断为COVID-19,鼻咽和口咽拭子逆转录聚合酶链反应试验呈阳性。COVID-19感染的危险因素包括男性(相对风险(RR) = 1.51;95%可信区间(CI), 1.15-1.99),体重指数(BMI)大于25 (RR = 1.03;95% CI, 1.01-1.05)和糖尿病(RR = 1.31;95% ci, 1.02-1.67)。吸烟(RR = 0.51;95% CI, 0.28-0.93)和教育程度(RR = 0.95;95% CI(0.92-0.98)呈负相关。结论男性、糖尿病患者和BMI超过25的人群应加强对COVID-19预防相关健康方案的认识和遵守,并应优先接种疫苗。
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引用次数: 2
The impact of quarantine on Covid-19 infections 隔离对Covid-19感染的影响
Q3 Mathematics Pub Date : 2021-02-01 DOI: 10.1515/em-2020-0038
P. Marshall
Abstract Objectives: Coronavirushas had profound effects on people’s lives and the economy of many countries, generating controversy between the need to establish quarantines and other social distancing measures to protect people’s health and the need to reactivate the economy. This study proposes and applies a modification of the SIR infection model to describe the evolution of coronavirus infections and to measure the effect of quarantine on the number of people infected. Methods: Two hypotheses, not necessarily mutually exclusive, are proposed for the impact of quarantines. According to the first hypothesis, quarantine reduces the infection rate, delaying new infections over time without modifying the total number of people infected at the end of the wave. The second hypothesis establishes that quarantine reduces the population infected in the wave. The two hypotheses are tested with data for a sample of 10 districts in Santiago, Chile. Results: The results of applying the methodology show that the proposed model describes well the evolution of infections at the district level. The data shows evidence in favor of the first hypothesis, quarantine reduces the infection rate; and not in favor of the second hypothesis, that quarantine reduces the population infected. Districts of higher socio-economic levels have a lower infection rate, and quarantine is more effective. Conclusions: Quarantine, in most districts, does not reduce the total number of people infected in the wave; it only reduces the rate at which they are infected. The reduction in the infection rate avoids peaks that may collapse the health system.
摘要目的:新冠肺炎疫情对许多国家人民的生活和经济产生了深远影响,引发了是否需要建立隔离等社会距离措施以保护人民健康与是否需要重振经济之间的争议。本研究提出并应用SIR感染模型的修改来描述冠状病毒感染的演变,并衡量隔离对感染人数的影响。方法:对隔离的影响提出了两种假设,但不一定相互排斥。根据第一种假设,隔离降低了感染率,随着时间的推移推迟了新的感染,而不会改变疫情结束时感染的总人数。第二种假设认为,隔离减少了波浪中的感染人口。这两种假设用智利圣地亚哥10个地区的样本数据进行了检验。结果:应用该方法的结果表明,所提出的模型很好地描述了地区一级感染的演变。数据显示支持第一种假设的证据,隔离降低了感染率;不支持第二个假设,隔离减少了感染人口。社会经济水平越高的地区,感染率越低,隔离效果越好。结论:大多数地区的隔离并没有减少疫情中感染的总人数;这只会降低他们被感染的几率。感染率的降低避免了可能导致卫生系统崩溃的高峰。
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引用次数: 6
Stepwise Markov model: a good method for forecasting mechanical ventilator crisis in COVID-19 pandemic 逐步马尔可夫模型:预测COVID-19大流行中机械呼吸机危机的好方法
Q3 Mathematics Pub Date : 2021-02-01 DOI: 10.1515/em-2020-0021
P. Olmos, G. Borzone
Abstract Objectives One important variable influencing day-to-day decisions in COVID-19 pandemic has been an impending shortage of mechanical ventilators due to the large number of people that become infected with the virus due to its high contagiousness. We developed a stepwise Markov model (a) to make a short-term prediction of the number of patients on ventilator, and (b) to determine a possible date for a ventilator crisis. Methods Starting with the exponential curve of new cases in the previous 14 days, we calculated a Markov model every 5 days thereafter, resulting in a daily estimate of patients on ventilator for the following 25 days, which we compared with the daily number of devices in use to predict a date for ventilator crisis. Results During the modeled period, the observed and predicted Markov curves of patients on ventilator were very similar, a finding confirmed by both linear regression (r=0.984; p<0.0001) and the near coincidence with the identity line. Our model estimated ventilator shortage in Chile for June 1st, if the number of devices had remained stable. However, the crisis did not occur due to acquisition of new ventilators by the Ministry of Health. Conclusions In Chile as in many other countries experiencing several asynchronous local peaks of COVID-19, the stepwise Markov model could become a useful tool for predicting the date of mechanical ventilator crisis. We propose that our model could help health authorities to: (a) establish a better ventilator distribution strategy and (b) be ready to reinstate restrictions only when necessary so as not to paralyze the economy as much.
摘要目的影响COVID-19大流行日常决策的一个重要变量是,由于病毒的高传染性导致大量人群感染,机械呼吸机即将短缺。我们开发了一个逐步马尔可夫模型(a)来对使用呼吸机的患者数量进行短期预测,(b)来确定呼吸机危机的可能日期。方法从前14天新增病例的指数曲线出发,每隔5天计算一个马尔可夫模型,得出未来25天每天使用呼吸机的患者数量,并将其与每天使用的设备数量进行比较,预测呼吸机危机发生的日期。结果在建模期间,观察到的呼吸机患者的马尔可夫曲线与预测的马尔可夫曲线非常相似,线性回归证实了这一结果(r=0.984;P <0.0001),与同一性线接近重合。我们的模型估计,如果设备数量保持稳定,6月1日智利的呼吸机短缺。然而,危机的发生并不是因为卫生部购置了新的呼吸机。在智利和其他许多经历了几次非同步局部COVID-19高峰的国家,逐步马尔可夫模型可能成为预测机械呼吸机危机日期的有用工具。我们建议,我们的模型可以帮助卫生当局:(a)建立更好的呼吸机分配策略,(b)准备在必要时恢复限制,以免严重瘫痪经济。
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引用次数: 1
Statistical modeling of the novel COVID-19 epidemic in Iraq 伊拉克新型COVID-19疫情的统计建模
Q3 Mathematics Pub Date : 2021-02-01 DOI: 10.1515/em-2020-0025
Ban Ghanim Al-Ani
Abstract Objectives This study aimed to apply three of the most important nonlinear growth models (Gompertz, Richards, and Weibull) to study the daily cumulative number of COVID-19 cases in Iraq during the period from 13th of March, 2020 to 22nd of July, 2020. Methods Using the nonlinear least squares method, the three growth models were estimated in addition to calculating some related measures in this study using the “nonlinear regression” tool available in Minitab-17, and the initial values of the parameters were deduced from the transformation to the simple linear regression equation. Comparison of these models was made using some statistics (F-test, AIC, BIC, AICc and WIC). Results The results indicate that the Weibull model is the best adequate model for studying the cumulative daily number of COVID-19 cases in Iraq according to some criteria such as having the highest F and lowest values for RMSE, bias, MAE, AIC, BIC, AICc and WIC with no any violations of the assumptions for the model’s residuals (independent, normal distribution and homogeneity variance). The overall model test and tests of the estimated parameters showed that the Weibull model was statistically significant for describing the study data. Conclusions From the Weibull model predictions, the number of cumulative confirmed cases of novel coronavirus in Iraq will increase by a range of 101,396 (95% PI: 99,989 to 102,923) to 114,907 (95% PI: 112,251 to 117,566) in the next 24 days (23rd of July to 15th of August 15, 2020). From the inflection points in the Weibull curve, the peak date when the growth rate will be maximum, is 7th of July, 2020, and at this time the daily cumulative cases become 67,338. Using the nonlinear least squares method, the models were estimated and some related measures were calculated in this study using the “nonlinear regression” tool available in Minitab-17, and the initial values of the parameters were obtained from the transformation to the simple linear regression model.
本研究旨在应用最重要的三种非线性增长模型(Gompertz、Richards和Weibull)研究2020年3月13日至2020年7月22日期间伊拉克COVID-19日累计病例数。方法利用Minitab-17中提供的“非线性回归”工具,在计算相关测度的基础上,采用非线性最小二乘法对3种生长模型进行估计,并将其转化为简单线性回归方程,推导出参数的初始值。采用f检验、AIC、BIC、AICc、WIC等统计数据对模型进行比较。结果从RMSE、bias、MAE、AIC、BIC、AICc和WIC的F值最高和最小等标准来看,威布尔模型是研究伊拉克新冠肺炎日累计病例数的最佳模型,模型残差(独立分布、正态分布和齐性方差)的假设没有任何违背。整体模型检验和估计参数检验表明,Weibull模型对研究数据的描述具有统计学显著性。根据威布尔模型预测,未来24天(2020年7月23日至8月15日),伊拉克新型冠状病毒累计确诊病例将增加101,396例(95% PI: 99,989至102,923)至114,907例(95% PI: 112,251至117,566)。从威布尔曲线的拐点来看,2020年7月7日为增长率最大的峰值日期,此时日累计病例为67,338例。本研究利用Minitab-17中提供的“非线性回归”工具,利用非线性最小二乘法对模型进行估计,并计算出一些相关测度,通过转换到简单线性回归模型得到参数的初始值。
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引用次数: 6
The first diffusion of the Covid-19 outbreak in Northern Italy: an analysis based on a simplified version of the SIR model 新冠肺炎疫情在意大利北部的首次扩散:基于SIR模型简化版的分析
Q3 Mathematics Pub Date : 2021-02-01 DOI: 10.1515/em-2020-0047
M. Magnoni
Abstract In this paper an analysis of the first diffusion of the Covid-19 outbreak occurred in late February 2020 in Northern Italy is presented. In order to study the time evolution of the epidemic it was decided to analyze in particular as the most relevant variable the number of hospitalized people, considered as the less biased proxy of the real number of infected people. An approximate solution of the infected equation was found from a simplified version of the SIR model. This solution was used as a tool for the calculation of the basic reproduction number R 0 in the early phase of the epidemic for the most affected Northern Italian regions (Piedmont, Lombardy, Veneto and Emilia), giving values of R 0 ranging from 2.2 to 3.1. Finally, a theoretical formulation of the infection rate is proposed, introducing a new parameter, the infection length, characteristic of the disease.
本文对2020年2月下旬在意大利北部发生的Covid-19疫情的首次传播进行了分析。为了研究流行病的时间演变,决定特别分析住院人数作为最相关的变量,因为住院人数被认为是实际感染人数的偏差较小的代理。从SIR模型的简化版本中找到了受感染方程的近似解。该溶液被用作计算受影响最严重的意大利北部地区(皮埃蒙特、伦巴第、威尼托和艾米利亚)疫情早期基本繁殖数r0的工具,r0的值在2.2至3.1之间。最后,提出了感染率的理论公式,并引入了一个新的参数,即感染长度和疾病的特征。
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引用次数: 2
Delaying the peak of the COVID-19 epidemic with travel restrictions 通过旅行限制推迟COVID-19疫情高峰期
Q3 Mathematics Pub Date : 2021-02-01 DOI: 10.1515/em-2020-0042
Kaare Græsbøll, L. Christiansen, U. H. Thygesen, C. Kirkeby
Abstract Objectives: Travel restrictions is an often-used tool for governments to prevent the spread of COVID-19. Methods: We here used a simple simulation model to investigate the potential effects of travel restrictions within a country. Results: We found that travel restrictions can delay the peak of the epidemic considerably, but do not affect the spread within the country. We also investigated the effect of implementing travel restrictions early or later in the epidemic, and found that fast implementation is crucial for delaying the epidemic. Conclusions: Fast implementation of travel restrictions is crucial for delaying the peak of a subsequent outbreak of COVID-19 within a country.
目的:旅行限制是各国政府预防新冠肺炎传播的常用工具。方法:我们在这里使用一个简单的模拟模型来调查一个国家内旅行限制的潜在影响。结果:我们发现旅行限制可以显著推迟疫情高峰,但不影响国内传播。我们还调查了疫情早期或后期实施旅行限制的效果,发现快速实施对延缓疫情至关重要。结论:快速实施旅行限制对于推迟一个国家后续COVID-19疫情的高峰至关重要。
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引用次数: 3
Covid-19: were curfews in France associated with hospitalisations? 2019冠状病毒病:法国的宵禁与住院有关吗?
Q3 Mathematics Pub Date : 2021-02-01 DOI: 10.1515/em-2021-0011
É. Le Bourg
Abstract Objectives A curfew was introduced in France in October 2020 to reduce the spread of Covid-19. This was done for two weeks in 16 departments, or for one week in 38 others, 42 departments not being subjected to the curfew. This article compares the number of new daily hospital admissions in these departments. Methods The ratio of the number of new hospitalisations during these two weeks and in the previous two weeks was computed in the three categories of departments. Results The increase in new hospitalisations was lower in departments under curfew for two weeks than in all other departments, and this result does not seem to be linked to characteristics of the departments before curfew. Conclusions This result shows that the two-week curfew is linked to a lower increase of hospitalisations, but not that the curfew by itself is the cause of this result, as other factors may have played a role.
2020年10月,法国实施宵禁,以减少Covid-19的传播。这在16个省实行了两周,在另外38个省实行了一周,42个省不实行宵禁。本文比较了这些科室每日新增住院人数。方法统计3类科室这2周新增住院人数与前2周新增住院人数之比。结果实施宵禁两周的科室新增住院人数增幅低于其他科室,这一结果似乎与宵禁前科室的特点无关。这一结果表明,为期两周的宵禁与住院率的较低增长有关,但并不是宵禁本身是导致这一结果的原因,因为其他因素可能也起了作用。
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引用次数: 0
COVID-19 effective reproduction number determination: an application, and a review of issues and influential factors COVID-19有效繁殖数的确定:一种应用,以及问题和影响因素的回顾
Q3 Mathematics Pub Date : 2021-02-01 DOI: 10.1515/em-2020-0048
L. A. Bautista Balbás, M. Gil Conesa, Blanca Bautista Balbás, G. Rodríguez Caravaca
Abstract Objectives An essential indicator of COVID-19 transmission is the effective reproduction number (R t ), the number of cases which an infected individual is expected to infect at a particular point in time; curves of the evolution of R t over time (transmission curves) reflect the impact of preventive measures and whether an epidemic is controlled. Methods We have created a Shiny/R web application (https://alfredob.shinyapps.io/estR0/) with user-selectable features: open data sources with daily COVID-19 incidences from all countries and many regions, customizable preprocessing options (smoothing, proportional increment, etc.), different MonteCarlo-Markov-Chain estimates of the generation time or serial interval distributions and state-of-the-art R t estimation frameworks (EpiEstim, R 0). This application could be used as a tool both to obtain transmission estimates and to perform interactive sensitivity analysis. We have analyzed the impact of these factors on transmission curves. We also have obtained curves at the national and sub-national level and analyzed the impact of epidemic control strategies, superspreading events, socioeconomic factors and outbreaks. Results Reproduction numbers showed earlier anticipation compared to active prevalence indicators (14-day cumulative incidence, overall infectivity). In the sensitivity analysis, the impact of different R t estimation methods was moderate/small, and the impact of different serial interval distributions was very small. We couldn’t find conclusive evidence regarding the impact of alleged superspreading events. As a limitation, dataset quality can limit the reliability of the estimates. Conclusions The thorough review of many examples of COVID-19 transmission curves support the usage of R t estimates as a robust transmission indicator.
目的有效繁殖数(R t)是COVID-19传播的一个重要指标,R t是一个感染者在特定时间点预计会感染的病例数;R - t随时间的演变曲线(传播曲线)反映了预防措施的影响以及流行病是否得到控制。我们已经创建了一个带有用户可选择功能的Shiny/R web应用程序(https://alfredob.shinyapps.io/estR0/):来自所有国家和许多地区的每日COVID-19发病率的开放数据源,可定制的预处理选项(平滑,比例增量等),不同的生成时间或序列区间分布的蒙特卡罗-马尔可夫链估计以及最先进的R t估计框架(EpiEstim, R 0)。该应用程序可以用作获得传播估计和执行交互式敏感性分析的工具。我们分析了这些因素对传输曲线的影响。我们还获得了国家和地方层面的曲线,并分析了流行病控制战略、超级传播事件、社会经济因素和疫情的影响。结果与活跃患病率指标(14天累计发病率、总传染性)相比,繁殖数显示出更早的预期。在敏感性分析中,不同的R t估计方法的影响均为中/小,不同序列区间分布的影响很小。关于所谓的超级传播事件的影响,我们找不到确凿的证据。作为限制,数据集质量会限制估计的可靠性。结论:对许多COVID-19传播曲线实例的全面审查支持使用R t估计值作为可靠的传播指标。
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引用次数: 0
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Epidemiologic Methods
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